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Leininger, Christopher Dunfield, Nathan Kapovich, Ilya Kent, Autumn Loving, Marissa Kawehi 2019-11-26T20:33:45Z 2019-11-26T20:33:45Z 2019-07-02 2019-08 "This thesis finds its roots in the Nielsen-Thurston classification of the mapping class group, a result that is fundamental to the field of low dimensional topology. In particular, Thurston's work gives us a powerful normal form for mapping classes: up to taking powers and restricting to subsurfaces, every mapping class can be decomposed into pieces which are either the identity or pseudo-Anosov. Associated to each of these pseudo-Anosov mapping classes is a unique algebraic number called its dilatation or ``stretch-factor"". In this thesis, we build on work of Penner who introduced the study of the minimal dilatation of pseudo-Anosovs in subgroups of the mapping class group. We prove upper and lower bounds on the minimal dilatation of pseudo-Anosovs in the $n$-stranded pure surface braid group extending results of Aougab--Taylor and Dowdall for the 1-stranded pure surface braid group." Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2019-11-26 without embargo terms The student, Marissa Loving, accepted the attached license on 2019-06-28 at 15:46. The student, Marissa Loving, submitted this Dissertation for approval on 2019-06-28 at 18:09. This Dissertation was approved for publication on 2019-07-02 at 17:21. DSpace SAF Submission Ingestion Package generated from Vireo submission #14110 on 2019-11-26 at 12:50:18 Made available in DSpace on 2019-11-26T20:33:45Z (GMT). No. of bitstreams: 3 LOVING-DISSERTATION-2019.pdf: 354278 bytes, checksum: 6f69d85f102503ee0755505292632b4c (MD5) Thesis - Marissa Loving (1).zip: 318511 bytes, checksum: 3f9bdf7d09f7e6937c05857cf0e96b31 (MD5) LICENSE.txt: 4211 bytes, checksum: 6790f517d20068e7b31028286ad812c6 (MD5) Previous issue date: 2019-07-02 application/pdf http://hdl.handle.net/2142/105626 en Copyright 2019 Marissa Kawehi Loving mapping class groups, pure surface braids, least dilatation, pseudo-Anosov Least dilatation of pure surface braids text text Mathematics Mathematics University of Illinois at Urbana-Champaign Dissertation Ph.D.